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Unformatted text preview: Economics 3010
Fall 2009 Professor Daniel Benjamin
Cornell University Problem Set 2 This problem set is due in section on Friday, September 18. Please collect your answers into a stapled packet, and write your own name and your TA’s name on the front of each packet. 0. (Aplia) Please do the assigned problems on the Aplia website. These problems are due at 11:45pm on Thursday, September 17. 1. (Preferences: Money pumps and safety in markets) [ The idea behind this question is directly from a recent research paper: Laibson, David I., and Leeat Yariv (2007), “Safety in markets: An impossibility theorem for Dutch books,” Caltech mimeo. If you are interested, feel free to read more details: http://www.hss.caltech.edu/~lyariv/Papers/DutchBooks.pdf ] (a) Naif is trying to decide what to buy for dessert. The possibilities are A (apple pie), B (brownies), or C (caramel ice cream). Naif has preferences over dessert and money. Some of her preferences between dessert and money are characterized by the following indifference relationships: A ~ $5 A ~ (B and $1) B ~ (C and $2) C ~ (A and $3) What does it mean if her preferences are complete and reflexive? (b) Assume that Naif’s preferences are complete and reflexive, and her preferences over money are monotonic. What can you conclude about her preferences between each possible pair of A, B, and C? What axiom do her preferences violate? Can you represent her preferences with a utility function? (c) A fellow named Arbitrageur realizes that he might be able to take advantage of Naif if he can get his hands on one each of A, B, and C. Suppose he can produce each at a cost of $4, so he goes ahead and pays $12 to produce an A, a B, and a C. Fill in the blanks to complete Arbitrageur’s strategy: (i) Sell A to Naif at a price of $4.99. (ii) Then offer to give __ to Naif if in exchange she gives him A and $2.99. (iii) Then offer to give B to Naif if in exchange she gives him __ and $1.99. (iv) Then offer to give A to Naif if in exchange she gives him B and $__. Would Naif agree to each of these steps? What is Arbitrageur’s profit (or loss) from steps (i)‐(iv), taking into account his costs of production? What if he kept repeating steps (ii) through (iv)? (d) Some economists have concluded that it is reasonable to assume people don’t have preferences like Naif’s because it is possible to take advantage of consumers like her (via a “money pump” like in part (c)). There are two versions of this argument. One version is that if somebody did her have preferences, that person would quickly go bankrupt and so wouldn’t have any effect on the economy. The second version is that if somebody did her have preferences, then we would see a lot of money pumps going on the real world; since we don’t see them, then nobody has those preferences. Choose one of these arguments, and explain it in a little more detail. (e) So far, we have been assuming that Arbitrageur is a monopoly supplier of goods A, B, and C to Naif – that is, there is no one else who is competing with Arbitrageur to provide those goods. Now suppose instead there is a competitive supply of goods A, B, and C to Naif – i.e., there are an infinite number of suppliers competing with each other to sell their goods to Naif. Assume that each supplier can produce A, B, and C at a cost of $4 (the same as Arbitrageur). Explain why Arbitrageur can now charge Naif no more than $4 for A. Explain why Arbitrageur cannot charge Naif anything anymore to make trades between A, B, C. (f) If Arbitrageur followed through with the sequence of trade from part (c) (but charging only as much as the market would allow), how much profit would he make? Explain why markets eliminate “money pumps” and thereby actually allow individuals like Naif to persist in having odd preferences. ...
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This note was uploaded on 12/28/2011 for the course ECON 3010 at Cornell University (Engineering School).
 '07
 WISSINK
 Microeconomics, Utility

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